Geometric sequences

Find $ a_7 $ of a geometric progression if $ a_1 = 15 ~~ \text{and} ~~ r = 1.5 $.

Find $ a_5 $ of a geometric progression if $ a_1 = 60 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 2 } $.

Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = 3 $.

Find the sum of the first $ 10 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -3 $.

Find the sum of the first $ 7 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = \frac{ 1 }{ 3 } $.

Find the sum of the first $ 12 $ terms of a geometric sequence if $ a_1 = 1 ~~ \text{and} ~~ r = -\frac{ 1 }{ 3 } $.

Find $ a_3 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 16 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.

Find $ a_15 $ of a geometric progression if $ a_1 = \dfrac{ 3 }{ 16 } ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.

Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = \frac{ 3 }{ 16 } ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.

Find $ a_4 $ of a geometric progression if $ a_1 = 320 ~~ \text{and} ~~ r = 4 $.

Find $ a_4 $ of a geometric progression if $ a_1 = 192 ~~ \text{and} ~~ r = -4 $.

Find $ a_4 $ of a geometric progression if $ a_1 = -375 ~~ \text{and} ~~ r = 5 $.

Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 200 ~~ \text{and} ~~ r = \frac{ 1 }{ 2 } $.

Find $ a_9 $ of a geometric progression if $ a_1 = 27 ~~ \text{and} ~~ r = 3 $.

Find $ a_16 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = -3 $.

Find $ a_11 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 3 $.

Find $ a_9 $ of a geometric progression if $ a_1 = 3 ~~ \text{and} ~~ r = -2 $.

Find $ a_19 $ of a geometric progression if $ a_1 = 14 ~~ \text{and} ~~ r = 1.5 $.

Find $ a_6 $ of a geometric progression if $ a_1 = 12 ~~ \text{and} ~~ r = -\dfrac{ 1 }{ 4 } $.

Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 12 ~~ \text{and} ~~ r = -\frac{ 1 }{ 4 } $.

Find $ a_10 $ of a geometric progression if $ a_1 = 13 ~~ \text{and} ~~ r = 3 $.

Find $ a_4 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 5 $.

Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 7 ~~ \text{and} ~~ r = 3 $.

Find $ a_3 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = \dfrac{ 103 }{ 100 } $.

Find $ a_11 $ of a geometric progression if $ a_1 = 256 ~~ \text{and} ~~ r = -2 $.

Find $ a_11 $ of a geometric progression if $ a_1 = 256 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.

Find the sum of the first $ 15 $ terms of a geometric sequence if $ a_1 = -3 ~~ \text{and} ~~ r = 2.4 $.

Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = \frac{ 5 }{ 8 } ~~ \text{and} ~~ r = -2 $.

Find $ a_8 $ of a geometric progression if $ a_1 = 320 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 2 } $.

Find the sum of the first $ 5 $ terms of a geometric sequence if $ a_1 = 280 ~~ \text{and} ~~ r = \frac{ 3 }{ 4 } $.

Find the sum of the first $ 9 $ terms of a geometric sequence if $ a_1 = \frac{ 56 }{ 5 } ~~ \text{and} ~~ r = \frac{ 8 }{ 5 } $.

Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 43 ~~ \text{and} ~~ r = 4 $.

Find the sum of the first $ 11 $ terms of a geometric sequence if $ a_1 = -192 ~~ \text{and} ~~ r = -\frac{ 4 }{ 3 } $.

Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = \frac{ 8 }{ 9 } $.

Find the sum of the first $ 6 $ terms of a geometric sequence if $ a_1 = 4 ~~ \text{and} ~~ r = 3 $.

Find the sum of the first $ 4 $ terms of a geometric sequence if $ a_1 = 2 ~~ \text{and} ~~ r = 9 $.

Find $ a_5 $ of a geometric progression if $ a_1 = -7 ~~ \text{and} ~~ r = 6 $.

Find the sum of the first $ 40 $ terms of a geometric sequence if $ a_1 = 10000 ~~ \text{and} ~~ r = 1.06 $.

Find $ a_40 $ of a geometric progression if $ a_1 = 10000 ~~ \text{and} ~~ r = 1.06 $.

Find common ratio ( $ r $ ) in geometic progression if $ a_1 = 9 ~~ \text{and} ~~ a_{ 3 } = 144 $.

Find $ a_7 $ of a geometric progression if $ a_1 = 100 ~~ \text{and} ~~ r = 1.06 $.

Find first element ( $ a_1 $ ) and a common ration ( $ r $ ) of a geometic progression if $ a_{ 3 } = 9 ~~ \text{and} ~~ a_{ 5 } = 81 $.

Find $ a_14 $ of a geometric progression if $ a_1 = 10 ~~ \text{and} ~~ r = 2 $.

Find $ a_1 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 2 $.

Find the sum of the first $ 8 $ terms of a geometric sequence if $ a_1 = 18 ~~ \text{and} ~~ r = \frac{ 2 }{ 3 } $.

Find $ a_43 $ of a geometric progression if $ a_1 = 2 ~~ \text{and} ~~ r = 0.85 $.

Find $ a_9 $ of a geometric progression if $ a_1 = 10000 ~~ \text{and} ~~ r = \dfrac{ 1 }{ 10 } $.

Find $ a_9 $ of a geometric progression if $ a_1 = 10000 ~~ \text{and} ~~ r = 0.1 $.

Find the sum of the first $ 20 $ terms of a geometric sequence if $ a_1 = 100 ~~ \text{and} ~~ r = 1.029 $.

Find $ a_15 $ of a geometric progression if $ a_1 = 4 ~~ \text{and} ~~ r = 3 $.